# Why does the derivation for the Michelson & Morley time difference assume Earth moves in only one direction relative to the Aether?

In the Michelson and Morley experiment, we predict with Galilean relativity and the assumption of the existence of a luminiferous aether that there should be a time difference between the two beams of light reaching the detector of an interferometer with arms of equal length. This time difference is given by:

$$\Delta t = \frac{2L}{c} (\gamma^2 - \gamma)$$

where $$\gamma$$ is the Lorentz constant, $$c$$ is the speed of light from the IRF of the aether, and $$L$$ is the length of the length of two arms of the interferometer.

This was derived under the assumption that the IRF of the experiment ("Earth") moves through the Aether at a velocity $$V$$ in a single direction as shown in the diagram below.

The derivation was similar to the derivation on Wikipedia page here which also uses this assumption. My question is, why is this assumption is allowed when surely the Earth could be moving with a velocity in the y-direction as well?

You can put the device anywhere on the earth, orient it any way that you want, and conduct the experiment at any time of the year. In some orientation of the device, the veclocity of the aether will be in the $$x$$ direction, and in this direction, you would expect the time of flight difference between the legs to be maximized.